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AUTHOR: 


CARUS,  PAUL 


TITLE: 


FORM  AND  FORMAL 
THOUGHT,.... 


PLACE: 


CHICAGO 


DA  TE : 


1889 


COLUMBIA  UNIVERSITY  LIBRARIES 
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j  108    Carus.  Paul  1852-1919  • 
Z2  Form  and  formal  thought,  the  fundamental 

problem  of  philosophy 
Chicago  1889       D  in  0      35  p 

Prom  his  ** Fundamental  problems'* 
No  3  of  a  vol  /   \   of  pamphlets 


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FORM-!-AND-:-FORMAL-:-THOUGHT. 


The  Fundamental  Problem  of  Philosophy 


BY 


^ 


DR.  PAUL  CARUS. 


EXCERPT  FROM   THE  WORK  ''  FUNDAMENTAL  PROBLEMS,"  PUB- 
LISHED SIMULTANEOUSLY  WITH  THE  APPEARANCE  OF 

THIS  PAMPHLET. 


1889]   J 


CHICAGO: 

THE  OPEN  COURT  PUBLISHING  COMPANY 

169-175  La  Salle  Street. 


V 


FORM  AND  FORMAL  THOUGIIt 


I. 

KANT'S    CRITIQUE   OF   PURE   REASON. 

• 

In  the  introduction  to  his  "Critique  of  Pure  Rea- 
son," Immanuel  Kant  proposes  the  question:  How  are 
synthetical  judgments  a  priori  possible?  On  the  so- 
lution of  this  problem  the  whole  structure  of  his  phil- 
osophy rests,  which  he  characterizes  as  Transcendental 
Idealism. 

'A  priori'  means  *  beforehand,'  and  its  opposite  *  a 
posteriori '  means  'afterwards.'  To  know  something 
a  priori  means  to  know  something  before  any  experi- 
ence thereof  has  been  had.  When  we  know  that  the 
specific  gravity  of  ebony  is  greater  than  that  of' water, 
we  can  declare  a  priori,  that  ebony  will  not  float,  but 
sink  to  the  bottom  (the  physical  law  being  also  con- 
sidered known).  rWe  can  even  know  it  before  the  ex- 
periment is  rtiade.  The  experiment  will  afterwards, 
I.  e,  a  posteriori,  verify  our  knowledge. 

This  is  the  general  meaning  of  the  terms  '  a  priori ' 
and  *a  posteriori.'  But  Kant  uses  the  words  in  a 
mgre  limited  sense. 

In  Kant's  language  the  te^m  'experience'  is  em- 
ployed to  signify  sense-perception.  It  is  not  ex- 
actly limited  to  that  meaning  throughout,  but  cer- 
tainly it  is  always  used  in  opposition  to  non-sensory  or 


2  FORM  AND  FORMAL  THOUGHT, 

mere  formal  knowledge.  That  which  produces  expe- 
rience, and  which  as  a  reality  outside  of  us  and  mde- 
pendent  of  our  sensation  corresponds  to  sensory  im- 
pressions. Kant  calls  'matter/  Therefore,  we  have 
knowledge  of  the  existence  of  matter  and  its  different 
properties  *  a  posteriori,'  or  from  experience,  i.  e.  from 
sense-perception  only. 

There  is  another  kind  of  knowledge,  however,  which 
is  not  sense-knowledge,  but  formal  knowledge.  Formal 
knowledge  can  be  gained  by  abstraction.   The  form  of 
ttiings,  such  as  globes,  cubes,  statues,  and  other  bodies, 
can  be  abstracted  from  their  material  reality.   We  can, 
for  instance,  think  away  all  things  in  the  world.  (We 
abstract  from  their  material  existence.)  What  is  left  is 
'empty  space';  and  this  conception  of  pure  space  is  the 
postulate  of  a  science   that  is    called    mathematics. 
We  can  abstract,  also,  from  all  processes  which  take 
place  in  the  world;  what  is  left  is  the  idea  of  duration 
only;   it  is  'empty  time,'   in   which  these  processes 
might  have  taken  place.   The  conception  of  time,  pure 
and  simple,  can  be  conceived  as  a  progress  through 
empty   units   without   reference  to   real  phenomena. 
Such  empty  units  are  called  numbers,  and  by  adding 
one  unit  to  another,  we  start  a  process  that  is  known 
as  counting.     Counting  is  the  basis  of  arithmetic.     If, 
again,  we  abstract  from  the  substance  of  our  thoughts, 
the  mere  forms  of  thought  remain,  which,  treated  as  a 
science,  are  called  formal  logic. 

It  must  be  remarked  in  passing  that  Kant  calls 
space  and  time 'pure  perceptions'  {reine  Anschauun^ 
gen),  while  the  categories  are  treated  as  *  pure  con- 
ceptions •  {reine  Verstandesbegriffe^  This  distinction 
is  justifiable  for  certain  purposes,  and  should  not  be 
slurred  over  by  commentators  of  Kant's  philosophy. 


^ 


FORM  AND  FORMAL   THOUGHT,  3 

However,  our  present  purpose  is  not  to  explain  or 
popularize  the  Critique  of  Pure  Reason,  but  to  use  its 
more  prominent  ideas  for  propounding  our  own  views 
which  grew  out  of  a  study  of  Kant's  Transcendental- 
ism. We  may  add  that  every  perception,  as  soon  as 
it  is  named  and  clearly  defined,  becomes  a  conception. 
Space  can  be  the  basis  of  mathematics,  and  time  of 
arithmetic  only  when  both  have  grown  to  be  clear  con- 
ceptions. 

Formal  knowledge  is  called  by  Kant  a  priori, 
because,  if  any  truth  of  these  formal  sciences  is 
established,  it  will  be  known  to  be  true  for  all  possi- 
ble cases  of  experience,  even  before  the  experiments 
have  been  made.  The  rules  of  mathematics,  of  arith- 
metic, and  logic,  possess  rigid  necessity  and  absolute 
universality.  They  are  the  condition  of  all  scientific 
investigation;  for  rigidity  and  universality  {Noi/iwen- 
digkeit  tind  Allgemeinheit)  in  experimental  sciences  can 
be  realized  only  through  the  assistance  of  the  formal 
sciences.  Astronomy  and  chemistry,  for  instance,  have 
become  sciences  only  by  the  application  of  mathemat- 
ics and  arithmetic;  and  where  can  any  kind  of  science 
be  found  that  could  dispense  with  logic? 

A  priori,  as  used  in  the  limited  sense  by  Kant,  is 
purely  formal  knowledge,  while  a  posteriori  is  iden- 
tical with  experience.  Marks  of  a  priori  truths  are,  ac- 
cording to  Kant,  absolute  rigidity  and  universality 
{Noihwendigkeii  und  Aiigemeinheii). 

Kant  has  been  represented  as  a  philosopher  who 
teaches  by  his  doctrine  of  the  a  priori,  that  man  has 
innate  ideas  ready  in  his  consciousness.  Pure  reason, 
he  was  supposed  to  believe,  wells  up  in  us  as  some 
mysterious  power  coming  from  trandescendent  and 
most  probably  supernatural  regions.  This  is  absolutely 


4  FORM  AND  FORMAL   THOUGHT. 

unfounded,  as  can  be  learned  from  the  very  first  sen- 
tence in  the  introduction  to  his  "Critique  of  Pure 
Reason": 

••  That  ail  our  knowledge  begins  with  experience  there  can  be  no 
••  doubt.  For  how  is  it  possible  that  the  faculty  of  cognition  shou'd 
••be  awakened  into  exercise  otherwise  than  by  means  of  objects 
••  which  affect  our  senses,  and  partly  of  themselves  produce  repre- 
••  sentations.  partly  rouse  our  powers  of  understanding  into  activity, 
••to  compare,  to  connect,  or  to  separate  these,  and  so  to  convert 
••  the  raw  material  of  our  sensory  impressions  into  a  knowledge  of 
••objects,  which  is  called  experience?*  in  respect  of  time,  there- 
of are,  no  knowledge  ef  ours  is  antecedent  to  experience,  but  begins 
**wiik  it." 

In  order  to  show  that  formal  knowledge  must  be 
distinguished  from  sensory  experience,  Kant  con- 
tinues: 

•'  But.  though  all  our  knowledge  begins  with  experience,  it  by 
••  no  means  follows,  that  all  arises  out  of  experience  f    For.  on  the 
••contrary,  it  is  quite  possible  that  our  empirical  knowledge  is  a 
"compound  of  that  which  we  receive  through  impressions,  and 
•■  that  which  the  faculty  of  cognition  supplies  from  itself  (sensory 
••  impressions  giving  merely  the  occasion),  an  addition  which  we 
♦•  cannot  distinguish  from  the  original  element  given  by  sense,  till 
"  long  practice  has  made  us  attentive  to.  and  skillful  in.  separating 
••it.     It  is.  therefore,  a  question  which  requires  close  investiga- 
••  tion,  and  is  not  to  be  answered  at  first  sight— whether  there  ex- 
••  ists  a  knowledge  altogether  independent  of  experience,  and  even 
••of  all  sensory  impressions?    Knowledge  of  this  kind  is  called  a 
••priori,  in  contradistinction  to  empirical  knowledge,  which  has  its 
••  sources  a  posteriori,  that  is,  in  experience." 

Formal  knowledge  is  independent  of  sensory 
experience  in  so  far  as  we  purposely  exclude  all 
sensory  experience.  But,  after  all,  inasmuch  as  sen- 
sory experience  is  the  beginning  of  all  knowledge,  a 
posteriori  as  well  as  a  priori,  to  that  extent  formal 

•  The  word  *  eiperience  '   is  here  used  in  the  popular  acceptation,  being 
taken  as  the  result  of  sensory  impressions  fashioned  by  pure  thouRht. 
t  Here  the  word  is  used  in  the  limited  sense,  as  sensory  experience. 


FORM  AND  FORMAL   THOUGHT.  5 

knowledge  is  dependent  upon  sensory  experience  (as 
Kant  emphatically  declares).  Experience  is  antece- 
dent in  time,  and  from  it  alone  formal  knowledge  can 
originate,  which— not  until  a  certain  height  of  mental 
development  has  been  reached  —  will  be  separated 
from  the  raw  material  of  sensory  impressions. 

Kant,  using  the  word  experience  in  the  limited 
sense  of  sensory  experience,  declares  that  investiga- 
tion must  go  beyond  experience  in  order  to  find  the 
laws  of  formal  knowledge,  or  pure  thought.  He,  there- 
fore, called  all  formal  knowledge  transcendental,  and 
speaks  of  transcendental  logic,  transcendental  dialec- 
tic, transcendental  mathematics,  and  transcendental 
arithmetic. 

Transcendental  is  by  no  means  transcendent. 
Transcendent  means  unknowable,  or  what  transcends 
knowledge;  transcendental,  according  to  Kant,  means 
what  transcends  experience.  It  is  not  unknowable, 
but,  on  the  contrary,  the  basis  of  all  knowledge,  and 
the  transcendental  sciences  treat  such  subjects  as  de- 
mand (if  treated  with  accuracy)  axiomatic  certainty. 
The  mysterious  has  no  place  in  the  realms  of  the 
transcendental. 

The  question  '  How  are  synthetical  judgments  a 
priori  possible?  '  is  to  the  same  purpose  as  another 
question  of  Kant's,  propounded  in  his  Prolegomena, 
§  36,  where  he  asks:  "How  is  nature  possible?" 
When  Kant  speaks  of  nature,  he  refers  to  our  concep- 
tion of  reality,  in  so  far  as  it  is,  or  can  become,  the  ob- 
ject of  science  representing  the  cosmical  order  of  na- 
ture. We  do  not  now  intend  to  enter  into  the  details 
of  the  problem,  as  to  how  far  we  agree  with  the  sage 
of  Konigsberg,  and  how  far  we  do  not  agree.  But 
it  seems  necessary  to  point  out  the  importance  of  the 


FORM  AND  FORMAL   THOUGHT, 


problem,  on  the  solution  of  which  the  possibility  of 
scientific  knowledge  depends. 

The  faculty  of  thinking  in  abstracio  is  called  rea- 
son; and  reason  (which  on  earth  man  alone  possesses 
by  virtue  of  language)  can  become  the  basis  of  sci- 
ence, if  by  a  critical  method  fallacies  and  vagaries  of 
reason  are  prevented.  Kant  says  in  the  introduction 
to  his  «  Critique  of  Pure  Reason  : " 

••The  critique  of  reason  leads  at  last,  naturally  and  neces- 
••sarily,  to  science;  and.  on  the  other  hand,  the  dogmatical  use  of 
••reason  without  criticism  leads  to  groundless  assertions,  against 
'•  which  others  equally  specious  can  always  be  set,  thus  ending  un- 
••  avoidably  in  skepticism." 

The  whole  book  is  devoted  to  this  critique.  It  shows 
that  pure  reason  (formal  thought)  is  limited  to  formal 
truths  only  and  cannot  contain  revelations  as  to  the 
substantial  (the  sensory  or  material)  contents  of  our 
conceptions.  This  should  have  been  self-evident,  but 
as  a  matter  of  fact,  philosophers  before  and  even  after 
Kant  have  most  confidently  asserted  much  about  God 
and  the  world,  the  human  soul,  innate  ideas,  and  other 
things,  while  their  whole  reasoning  rested  upon  unwar- 
ranted a  priori  arguments.  Such  philosophers  Kant 
calls  dogmatical.  Wolf  (i679-i754)»  who  had  most 
methodically  systematized  the  metaphysical  doctrines 
of  his  time,  is  the  most  representative  dogmatic  phi- 
losopher. 

If  we  compare  our  cognition  to  building  material, 
Kant  said,  our  transcendental  knowledge  has  been  em- 
ployed by  dogmatical  philosophers  for  erecting  a  lofty 
dome  that  should  reach  to  Heaven.  For  this  purpose 
the  "  Critique  of  Pure  Reason  "  has  found  the  materir 
als  insufficient.  Nevertheless,  our  transcendental  cog- 
nition is  most  valuable;  certainly  it  is  unfit  for  the 


FORM  AND  FORMAL   THOUGHT, 


airy  castles  of  supernatural  systems;  but  if  employed 
for  its  proper  purpose,  Kant  continues,  "  it  very  well 
suffices  for  a  mansion  here  on  earth  spacious  enough 
for  all  our  purposes  and  high  enough  to  enable  us  to 
survey  the  level  plain  of  experience." 

Formal  cognitions,  or  conceptions  a  priori,  are  of 
themselves  "  empty; "  and  sensory  impressions  of 
themselves  are  *'  blind."  If  we  had  only  unconnected 
sensory  impressions,  we  would  be  worse  off  than  the 
lowest  animalcula  or  even  plants,  and  the  materials  of 
our  experience  received  through  our  sensory  organs 
would  be  of  no  avail.  Our  formal  cognitions  furnish  the 
mortar,  as  it  were,  of  a  synthetic  method  which  will 
enable  us  to  arrange  sensory  impressions  in  compre- 
hensively arranged  systems.  Formal  cognition  and 
sensory  experience,  therefore,  are  the  warp  and  woof 
of  scientific  knowledge.  The  warp  as  well  as  the  woof, 
each  by  itself,  consists  of  single  threads,  but  in  their 
combination  they  will  furnish  a  well-woven  fabric. 

If  a  philosopher  limits  his  method  to  sensory  experi- 
ence alone,  he  will  never  attain  scientific  certainty;  he 
can  never  make  definite  and  positive  statements,  but 
will  only  propose  opinions  which  may  be  overturned 
on  the  slightest  occasion.  Such  a  one-sided  empiri- 
cal, or  naturalistic,  philosopher  would  be  guilty  of  the 
opposite  error  of  the  dogmatist,  and  while  the  dogma- 
tist ultimatel}^  must  arrive  at  futile  assertions,  the  em- 
piricist's mere  opinions  must  lead  directly  to  skepticism. 
As  the  representative  philosopher  of  skepticism,  Kant 
mentions  David  Hume.  David  Hume  does  not  recog- 
nize the  difference  between  formal  knowledge  and 
sensory  experience.  To  him,  therefore,  all  knowl- 
edge consists  of  single,  unconnected  threads  of  knowl- 
edge. 


d 


PORM  AND  FORMAL   THOUGHT, 


On  the  last  two  pages  of  Kanfs  "Critique  of  Pure 
Reason/'  we  read  the  following  passages: 

"  We  may  divide  the  methods  at  present  employed  in  the  field 
••of  enquiry  into  the  naturalistic  and  the  scientistic." 

'  'Naturalistic'  here  means  what  is  commonly  called 
«  common  sense  philosophy,"  which,  repudiating  all 
speculation,  does  not  feel  the  need  of  a  critical 
method.    Kant  continues: 

"The  naturalist  of  pure  reason  lays  it  down  aS  his  principle, 
•*  that  common  reason,  without  the  aid  of  science— which  he  calls 
••sound  reason,  or  common  sense — can  give  a  more  satisfactory 
"  answer  to  the  most  important  questions  of  metaphysics  than  spec- 
*•  Illation  is  able  to  do.  He  must  maintain,  therefore,  that  we  can 
••determine  the  content  and  circumference  of  the  moon  more 
••  certainly  by  the  naked  eye  than  by  the  aid  of  mathematical  rea- 
••  soning.  But  this  system  is  mere  misology  [contempt  of  rational 
"thought]  reduced  to  principles;  and,  what  is  the  most  absurd 
'•  thing  in  this  doctrine,  the  neglect  of  all  scientific  means  is  paraded 
"as  a  peculiar  method  of  extending  our  cognition.  As  regards 
"  those  who  are  naturalists  because  they  know  no  better,  they  are 
•'  certainly  not  to  be  blamed.  They  follow  common  sense,  with- 
•'  out  parading  their  ignorance  as  a  method  which  is  to  teach  us  the 
"  wonderful  secret,  how  we  are  to  find  the  truth  which  lies  at  the 
•'  bottom  of  the  well  of  Democritus." 

'Scientistic'  denotes  here  the  method  of  one-sided 
scientists.  The  original  German  text  reads  scienii- 
fisch,  which  has  been  coined  by  Kant  in  opposition  to 
wissenshaftsHchy  /.  e,  scientific  in  its  usual  sense.  This 
scientistic,  or  one-sided  scientific,  method  lacks  cri- 
tique; it  does  not  distinguish  between  formal  and  sen- 
sory (between  a  priori  and  a  posteriori),  and  must 
either  undervalue  the  importance  of  formal  cognition, 
by  not  properly  employing  it  as  a  synthetic  principle, 
or  overvalue  the  importance  of  formal  cognition  by  at- 
tributing to  it  the  power  of  a  supernatural  revelation. 
Kant  continues,  and  concludes  his  "  Critique  of  Pure 
Reason  "  as  follows: 


FORM  AND  FORMAL   THOUGHT.  9 

"As  regards  those  who  wish  to  pursue  a  scientistic  method,  they 
have  now  the  choice  of  following  either  the  dogmatical  or  the 
skeptical,  while  they  are  bound  never  to  desert  the  systematic 
mode  of  procedure.  When  I  mention,  in  relation  to  the  former, 
the  celebrated  Wolf,  and  as  regards  the  latter,  David  Hume,  I 
may  leave,  in  accordance  with  my  present  intention,  all  others 
unnamed. 

"The  critical  path  alone  is  still  open.  If  my  reader  has 
been  kind  and  patient  enough  to  accompany  me  on  this  hith- 
erto untraveled  route,  he  can  now  judge  whether,  if  he  and  oth- 
ers will  contribute  their  exertions  towards  making  this  narrow 
foot-path  a  high-road  of  thought,  that,  which  many  centuries 
have  failed  to  accomplish,  may  not  be  executed  before  the  close 
of  the  present— namely,  to  bring  Reason  to  perfect  contentment 
in  regard  to  that  which  has  always,  but  without  permanent  re- 
sults, occupied  her  powers  and  engaged  her  ardent  desire  for 
knowledge." 


11. 
THE  ORIGIN  OF  THE  'A  PRIORI.' 

Kant  answers  the  question  '  How  are  synthetic 
judgments  a  priori  possible?'  by  showing  that  such 
synthetic  judgments  undoubtedly  exist. 

A  synthetic  judgment  is  different  from  an  analytic 
judgment.  An  analytic  judgment  merely  analyses 
knowledge  and  contains  nothing  but  an  explanation  or 
elucidation  of  what,  in  an  involved  form,  we  have 
known  before,  but  a  synthetic  judgment  really  ampli- 
fies our  knowledge;  it  adds  to  the  stock  of  our  knowl- 
edge something  new,  which  we  have  not  known  be- 
fore. In  proving  that  the  exterior  angle  of  a  triangle 
is  equal  to  the  sum  of  the  two  opposite  interior  angles 
of  the  same,  we  amplify  our  knowledge  of  the  triangle 
by  mere  ratiocination,  a  priori.  Kant  uses  even  a  sim- 
pler instance.  The  judgment  7  +  5  :=  12  is  not  analytic 


lO 


FORM  AND  FORMAL   THOUGHT, 


but  synthetic.     The  concept  twelve    is   neither  con- 
tained in  seven  nor  in  five,  but  is  something  entirely 

new. 

Kant  leaves  the  subject  here  and  is  satisfied  with 
the  fact  thai  synthetic  judgments  a  priori  are  possible. 
He  might  have  ventured  a  step  further  by  pro- 
posing another  question:  *What  is  the  origin  of  the 
a  priori?'  Only  by  answering  this  question  could  he 
have  shown,  hmo  synthetic  judgments  a  priori  are 
possible.  This  he  did  not  do,  and  the  omission  has 
produced  great  confusion  among  German,  French, 
and  English  thinkers. 

The  word  *a  priori'  is  undoubtedly  an  old-fash- 
ioned and  awkward  expression,  which  has  not  yet  lost 
the  savor  of  *  innate  ideas.'  It  was  readily  accepted  in 
England  by  philosophers  of  a  theological  bias  who 
were  little  aware  of  the  dangerous  properties  concealed 
in  this  Kantian  idea.  It  sounds  so  scholarly  Latin, 
almost  ecclesiastical;  for  it  is  an  expression  handed 
down  from  mediaeval  times.  But  when  they  drew  this 
clumsy  wooden  horse  within  the  walls  of  their  dog- 
matic stronghold,  they  unwittingly  admitted  an  army 
of  bellicose  warriors— Kant's  critical  thoughts— who 
are  sure  to  conquer  and  destroy  the  citadel  of  dualistic 

orthodoxy. 

'*  The  old  fashioned  a  priori  in  science,  in  morals, 
and  religion,"  a  reviewer  in  Science"^  somewhere  re- 
marks  "used  to  be  represented  as  an  arrogant  and  in- 
tolerant thing,  mysterious  in  its  manner  of  speech,  vi- 
olent and  dogmatic  in  the  defense  of  its  own  claims. 
The  English  Empiricists  used  to  hate  this  aristocratic 
a  priori  and  they  shrewdly  suspected  it  to  be  a  hum- 
bug.    What  they  gave  us  in  its  place,  however,  was  a 

•  SCI«IIC«.      Vol.  V,  p.  202. 


# 


FORM  AND  FORMAL   THOUGLLT.         ii 

vague  and  unphilosophic  doctrine  of  science  that  you 
could  only  seem  to  understand  so  long  as  you  did  not 
examine  into  its  meaning."  J.  S.  Mill's  philosophy 
moved  in  a  circle.  "  He  had  founded  all  inductive  in- 
terpretation of  nature  on  the  causal  principle  and  the 
causal  principle  again  on  an  inductive  interpretation 
of  nature."  , 

Kant,  as  we  have  stated,  calls  the  a  priori  truths 
'formal  knowledge,'  and  this  indicates  that  the  gen- 
eral postulates  of  the  transcendental  sciences,  the  ax- 
iomatic conceptions  from  which  they  start,  are  ab- 
stracted from  reality  by  thinking  away,  as  it  were, 
their  material  existence,  which  is  represented  in  our 
sensory  impressions.  Kant  suggests  this  conception 
of  the  a  priori,  but  he  nowhere  pronounces  it.  On 
the  contrary,  he  makes  statements  which  may  be  taken 
to  exclude  this  interpretation  of  his  conception. 

According  to  our  view,  form  is  a  property  of  re- 
ality as  well  as  of  our  cognition.  Formless  matter 
does  not  exist.  Form  and  matter,  as  they  exist  in 
reality,  are  inseparable.  What  is  called  formless 
matter  is  either  uniform  or  lacking  that  kind  of  form 
v/hich,  in  our  opinion  or  according  to  our  wishes,  it 
should  have.  Knowledge  also  in  its  primitive  shape, 
when  it  is,  so  to  say,  natural  and  crude,  is  an  intimate 
combination  of  sense-perceptions  and  formal  cognition. 
The  sense-perceptions  are  the  real  substance  of  knowl- 
edge, while  formal  cognition  is  the  principle  which  ar- 
ranges and   systematizes   sense-experience. 

As  soon  as  a  living  being  develops  the  ability  to 
think  in  abstracto,  a  state  which  is  attained  by  means 
of  language,  he  can  think  of  different  qualities  inde- 
pendent of  things.  He  can  think  of  whiteness,  of  great- 
ness, of  smallness,  of  courage,  and  of  cowardice.  And 


L  I 

i 


12        FORM  AND  FORMAL   THOUGftl, 

soon  after  that,  he  will  be  also  able  to  think  one,  two, 
three,  four,  five  units  in  abstracto  without  the  as- 
sistance of  his  fingers;  he  will  count.  Counting  is  a 
most  important  step  in  the  development  of  humanity, 
for  it  is  the  first  purely  formal  thought.  It  abstracts 
from  the  objects  counted  and  refers  exclusively  to  the 
unit  numbers  which  then  may  be  employed  for  any 
kind  of  things. 

Physiologically  considered  the  growth  of  abstract  and 
formal  ideas  must  have  developed  in  the  following  way: 

Irritations  in  the  amoeba  can  only  produce  vague 
feelings.  Light  and  darkness,  heat  and  cold,  moist- 
ure and  aridity,  abundance  and  scarcity  of  food,  ex- 
ercise a  certain  influence  upon  the  animalcule;  they 
act  upon  it  in  a  certain  way  and  produce  more  or  less 
favorable  or  unfavorable  effects  in  the  living  substance 
which  may  ultimately  result  in  reactions  of  some 
kind.  In  higher  animals  irritations  are  reacted  upon 
differently  in  different  organs.  Sensitiveness  has  been 
differentiated,  and  a  ray  of  light  is  perceived  on  the 
nerves  of  the  skin  as  warmth  and  in  those  of  the  eye 
as  light. 

The  same  process  of  differentiation  and  speciali- 
zation takes  place  in  the  brain.  If  a  horse  is  seen,  its 
image  appears  on  the  retina  of  the  eye,  whence  the 
irritation  is  transmitted  through  the  optic  nerve  to  the 
interior  parts  of  the  brain.  There  it  is  perceived  as  a 
horse.  According  to  Hering*  and  other  physiologists, 
there  is  no  doubt  but  that  every  new  perception  of  a 
horse  is  registered  on  the  same  spot  in  the  brain  as 
previously.  Every  single  brain-cell  has  a  memory  of 
its  own,  which   makes  it  more  fit  to  be  irritated  by 


FORM  AND  FORMAL   THOUGHT. 


13 


% 


^ 


*■  See  Ewald  Hering;  Memory  as  a  General  Function  of  Organized  Matter 
The  Open  Court,  p.  143. 


that  perception  to  which  it  has  adapted  itself.  Thus, 
the  conception  of  a  horse  is  the  sum  total  of  all  per- 
cepts of  a  horse.  It  is,  as  Mr.  Hegeler  *  most  appro- 
priately expresses  it,  like  a  composite  photograph. 
The  common  features  of  a  certain  group  of  same| 
things  are  preserved,  while  the  individual  traits  be- 
come blurred  and  are  lost  sight  of. 

Thus  the  many  varying  images  of  the  eye,  and  all 
sensory  impressions,  as  well  as  motory  exertions,  are 
registered  somewhere  in  the  brain,  each  kind  in  its 
place.  The  special  memory  of  the  different  fibres  and 
cells  naturally  arranges  all  percepts  and  concepts  in 
a  proper  order.  Moreover,  a  repeated  simultaneous- 
ness  of  different  sensations  which  are  produced  by 
same  causes  in  different  sense-organs,  produces  asso- 
ciations between  certain  percepts.  We  think  of  the 
rose  and  at  the  same  time  of  its  smell  and  its  color. 
We  see  a  bird  and  think  of  his  song,  and  the  dog  who 
sees  the  whip  feels  at  once  in  his  recollection  the 
pain  caused  by  its  lash. 

Horses  have  been  perceived  which  are  different  in 
size,  and  color,  and  temper,  etc.  These  differences 
are  occasionally  of  importance.  A  horse  may  attract 
attention  because  it  is  as  white  as  snow.  The  horse 
is  perceived  and  also  its  whiteness.  Thus  a  new  con- 
cept is  created,  the  concept  of  a  quality  which  does 


*  Mr.  E.  C.  Hegeler,  in  his  essay,  "The  Soul,"  (see  The  Open  Court,  p. 
393)  ^ays: 

"  If  an  abstraction  is  made,  many  thin^^s  having  something  in  common  are 
put  together,  and  what  they  have  in  common  is  specified  in  words.  It  is  then 
forgotten  that  what  they  do  not  have  in  common  disappears  in  the  generaliza- 
tion. The  same  takes  place  in  Gallon's  composite  photographs  of  the  mem- 
bers of  a  family.  Only  that  remains  of  the  several  faces  what  they  have  in 
common.  This  implies  that  the  composite  photograph  is  entirely  contained 
in  each  of  the  single  photographs  of  each  member,  each  is  the  complete  com- 
posite with  additions.  So  in  reality  the  composite  photograph  is  an  abstraQ- 
tion— a  part — of  each  of  the  single  photographs." 


14         FORM  AND  FORMAL    THOUGHT. 

not  correspond  to,  but  has  been  abstracted  from,  con- 
crete objects.  White  roses,  white  snow,  white  stones 
(as  lime  or  chalk),  and  white  horses  have  been  per- 
ceived, and  the  percept  of  *  whiteness'  is  produced,  to 
which  again  a  special  province  of  the  brain  must  be 
ascribed,  which  of  course  must  be  connected  by  nerve 
fibres  with  all  white  things,  more  so  with  things  that 
are  always  white  than  with  those  that  appear  so  only 
occasionally.  The  psychical  connection  of  such  con- 
cepts is  called  association. 

Suppose  we  are  in  a  library  where  the  books  are 
well  arranged  by  a  number  of  librarians  who  have  dif- 
ferent but  each  one  his  own  special  interests.  Many 
books  are  being  constantly  delivered.  There  are 
books  about  horses,  and  dogs,  and  flowers,  and 
stones,  etc.,  etc.  Every  librarian  takes  the  books 
of  that  subject  with  whose  study  he  is  specially  en- 
gaged and  places  it  in  his  alcove.  The  library  would 
be  in  the  best  order,  and  yet  so  long  as  the  different  al- 
coves were  not  named,  most  of  its  treasures  would  be 
inaccessible  for  many  most  important  purposes.  Such 
is  the  arrangement  in  animal  brains.  A  dog  knows 
what  a  cat  is.  Every  new  perception  of  a  cat  awakens 
in  his  mind  with  more  or  less  vividness  all  the 
many  previous  percepts  of  a  cat  with  their  different 
associations,  mostly  memories  of  pursuit,  perhaps  also 
of  resistance  and  combat.  But  all  these  memories  are 
single  percepts.  They  have  not  yet  coalesced  into 
a  unitary  and  clear  conception  of  catdom.  If  the  sum 
total  of  the  cat-percepts  in  his  memory  is  to  be  called 
a  conception,  it  is  certainly  a  very  imperfect  kind  of 
conception.  A  conception  becomes  distinct  only  by 
being  named.  This  is  the  truth  which  has  been  so 
splendidly  elucidated  by  our  best  philological  authori- 


f 


/ 


FORM  AND  FORMAL   THOUGHT 


15 


ties,  namely,  that  thought  (the  abstract  thought  of 
reasonable  beings)  is  only  possible  by  the  help  of  lan- 
guage. Man  thinks  because  he  speaks.  The  name 
of  a  thing  is,  as  it  were,  a  string  tied  around  all  the 
many  percepts  of  that  thing,  thus  comprehending  them 
all  in  one  concept.  Concept  is  derived  from  con  and 
capio  and  means,  according  to  its  etymology,  a  taking 
oi^  grasping  together,  a  gathering  into  and  holding  in 
one. 

The  act  of  naming  is  therefore  an  enormous 
economy  in  mental  activity;  it  is  the  mechanical 
means  by  which  abstract  ideas  or  generalizations  are 
formed;  and  the  faculty  of  thinking  in  abstracto  is 
called  reason.  Reason,  therefore,  in  its  elementary 
origin,  is  abstracting  and  combining.  Abstracting  is 
a  kind  of  separation.  We  separate  the  quality  of  white 
from  white  objects  and  combine  all  the  different  white- 
sensations  into  one  concept  by  the  name  of  'whiteness.' 
Both  processes,  that  of  separation  and  of  combination, 
are  essential  features  of  reason;  but  they  are  the  es- 
sential features,  and  all  functions  of  reason  can  be 
reduced  to  these   two  processes.* 

Our  brain  is  like  a  workshop  in  full  and  unceasing 
activity.  In  its  operation,  we  i^ust  distinguish  three 
things: 

•  F.  Max  Miillcr  defines  Reason  as  '•addition  and  subtraction."  We  have 
repeatedly  given  our  full  assent  to  the  great  philologist's  views  with  the  re- 
mark, that  we  should  substitute  for  "  addition  and  subtraction  "  the  terms  used 
above,  i.  e.,  "combination  and  separation."  The  terms  "  addition  and  sub- 
traction "  are  confined  to  arithmetic;  and  to  our  mind  they  are  different  from 
"combination  and  separation  "  in  so  far  as  "  subtraction  "  is  used  of  units  that 
are  taken  away  from  other  equal  units,  while  "  separation  "  takes  a  part  from 
something  that  appeared  as  a  unit  (an  integral  whole)  before  the  separation. 
Similarly  an  addition  sums  up  units  of  the  same  kind  (or  at  least  those  which 
for  the  purpose  of  addition  are  considered  as  being  of  the  same  kind)  into  a 
larger  number,  while  a  combination  unites  parts  into  one  consolidated  whole. 
We  believe  that  there  is  no  substantial  difference  between  Prof.  Max  Muller's 
view  and  our  own. 


i6         l^ORM  AND  FORMAL   THOUGHT. 


.w  J 


KMa 


irr% 


I 


1.  The  activity  which  is  called  life;  it  is  a  special 
kind  of  energy.  Its  presence  makes  itself  felt  as  mo- 
tion, which  is  a  change  of  place  and  could  be,  if  all  de- 
tails were  known,  mechanically  expressed. 

2.  The  material  of  which  the  whole  workshop  of 
the  brain  consists,  and  which  is  used  to  keep  it  in 
working  order;  viz.,  the  matter  which  is  constantly 
combining  and  decomposing  in  the  protoplasm  of  the 
brain-substance. 

3.  The  form  in  which  life  operates  in  the  nervous 
substance.  Every  brain-cell  has  a  special  form,  the 
groups  of  cells  are  arranged  in  special  forms  and  the 
whole  system  of  the  different  cerebral  organs  is  built 
up  in  a  special  form. 

We  distinguish  these  three  things,  but  in  reality 
they  are  inseparably  united.  If  our  percepts  and  con- 
cepts are  to  be  physically  considered,  they  should  not 
be  represented  as  the  activity  only  of  the  brain,  nor  as 
brain-substance,  nor  as  their  mere  form.  They  are  ac- 
tivity, and  matter,  and  form  united;  being  a  special 
form  of  the  activity  in  brain-substance.  It  goes  without 
saying  that  the  form  of  a  special  energy  depends  upon 
the  form  of  that  substance  in  which  the  process  takes 
place.  The  form  of  a  motion  and  the  form  of  the  sub- 
stance in  which  the  motion  takes  place,  are  not  only 
interdependent,  they  are  identical. 

A  certain  percept,  being  a  special  form  of  motion  in 
living  brain  substance,  leaves  in  those  cells  in  which  it 
takes  place,  such  vestiges  as  to  produce  a  disposition 
adapted  not  only  to  receive  the  same  or  similar  per- 
cepts, but  even  to  reproduce  that  percept  spontane- 
ously, if  the  cells,  nourished  by  the  blood-circulation, 
are  stimulated  into  activity  through  some  inner  pro- 
cess by  association.     This  disposition   (called  by  He- 


o 


h 


FORM  AND  FORMAL   THOUGHT.         17 

ring  Stimmung,  which  is  produced  by  the  special  mem- 
ory of  organized  matter),  becomes  stronger  by  repe- 
tition and  thus  imparts   more    and  more  stability  to 

that  special  form. 

Physiologically  considered,   percepts  and  concepts 
are  very  complicated  structures  which  in  their  asso- 
ciations may  resemble  a  kind  of  three-dimensional  net- 
work, showing  interlacings  of  innumerable  star-shaped 
knots,  the  threads  of  which  interradiate  and  combine 
the  various  sensory  percepts  belonging   to  the  same 
idea.     But   for  the   sake  of  simplicity  let  us  suppose 
that  perceptions  and  conceptions  grew  in  a  brain  like 
cells  and  groups  of  cells  simply;  they  would  naturally 
and  mechanically  arrange  themselves  in   systematic 
order.     One  of  the  first  steps  in  the  evolution  of  living 
matter  is  that  of  giving  stability  to  its  outer  form  by 
enveloping  itself  in  a  membrane.    Form,  as  we  under- 
stand the  term,  is  not  only  the  outside  shape,  but  also 
the  inner  disposition  and  arrangement  of  atoms.  How- 
ever, for  the  sake  of  simplicity  again,  and  as  a  matter 
of  crude  illustration,  let  us  for  a  moment  use  the  mem- 
branes of  cells  as  an  example  of  their  forms.     The 
membranes  of  cells  are  also  organic  substance  and  their 
material  particles  are    constantly  changing.     Never- 
theless,   they   possess  a  relative  stability  which  rep- 
resents the  shape  of  the  cells,  /.  e.,  their  outer  form. 
If  we  would  take  out  of  such  a  brain  the  living  sub- 
stance without  destroying  the  membranes  in  which  the 
cells  have  enveloped  themselves,  it  would  afford  an 
aspect  of  divisions  and  subdivisions  not  unlike  that  of 
the  departments,  shelves,  and  pigeon  holes  of  a  library 
from  which  the  books  are  removed,  and  we  would  have 
an  anatomical  representation  of  a  system  of  formal 
thought. 


i8 


FORM  AND  FORMAL   THOUGHT. 


It  is  understood  that  this  explanation  is  a  simile 
only  to  show  that  form  grows  pari  passu  with  its  sub- 
stance, and  mere  form,  if  abstracted  from  its  sub- 
stance, is,  for  purposes  of  thought,  by  no  means  value- 
less; it  is  of  greatest  importance  for  a  proper  orien- 
tation among  the  enormous  mass  of  sense-perceptions 
that  crowd  upon  the  mind. 

An  animal  and  a  man  may  have  the  very  same  sen- 
sory impressions;  their  brain  substance  consists  of  the 
same  combinations  of  nervous  matter;  sensations  (the 
basis  of  all  mental  activity)  are  produced  by  the  same 
kind  of  organs  and  in  the  same  way.  Yet  there  is  a 
difference  of  form  between  the  animal  and  the  human 
brain  in  so  far  as  the  many  different  impressions 
of  same  percepts  have  not  yet  attained  in  the  an- 
imal  brain  that  stability  and  unity  which  they  pos- 
sess  in  the  hu„,an  brain  In  the  human  brain  the  sub- 
divisions are  more  marked,  the  furrows  are  deeper  as 
well  as  more  numerous;  and  from  recent  investigations 
we  know  that  every  class  of  same  perceptions  has  ac- 
quired an  additional  and  closely  associated  brain 
Structure  which  embodies  its  name.*  The  whole  group 
of  certain  percepts  together  with  their  name  repre- 
sents what  in  logical  and  psychological  language  is 
called  a  concept. 

Let  us  now  suppose  that  the  chief  librarian  of  the 
library  of  our  brains  for  the  sake  of  arranging  a  cat- 
alogue takes  an  inventory  of  all  the  books  arranged  in 
the  different  alcoves.  He  would  find  the  same  prin- 
ciple of  arrangement  applied  everywhere.     The  differ- 

*  Compare  the  map  and  explanations  of  the  human  brain  in  Ehr  MentcM, 
by  Dr.  Johannes  Ranke,  Vol.  I,  p.  530  et  seq.  The  chapter,  '*  I^kaltsatiam  in 
der  Crauen  Gr&ssbirnrinde,^'  explains  Broca's,  Hitzig's,  and  Fritsch's  inves- 
tigations. It  takes  into  consideration  the  arguments  proposed  by  adversaries 
of  the  localization  theory  (Goitz,  etc.),  and  adopts  Exner'a  view  which,  it  ap- 
pears, reconciles  seeminfEly  irreconcilable  principles. 


FORM  AND  FORMAL   THOUGHT. 


19 


ent  alcoves  would  have  separate  departments  and  these 
again  would  be  found  to  possess  subdivisions.  This 
kind  of  arrangement,  which,  as  we  stated  above,  grew 
naturally,  became  first  apparent  when  the  process  of 
naming  took  place.  Many  different  names  were  con- 
ceived in  our  consciousness  to  be  special  kinds  of  one 
general  kind  so  that  they  together  formed  one  system 
of  ideas.     Logicians  call  it  genera  and  species. 

The  librarian  (we  now  suppose)  arranges  an  office 
(perhaps  for  the  purpose  of  reference)  in  which  a  gen- 
eral plan  of  the  whole  library  can  be  found.  This  ref- 
erence room  contains  no  books.  The  visitor  finds  there 
no  substantial  information;  the  information  to  be 
gained  there  is  purely  formal  and  serves  the  purpose 
to  find  one's  way  easier  in  the  many  different  depart- 
ments of  the  alcoves.  This  reference  room  in  our  brain 
is  called  logical  ability,  or  mathematical  reasoning,  or 
calculation,  and  we  need  not  say  that  its  establishment 
marks  another  important  step  in  the  development  of 
reason;  it  is  formal  thought.  It  is  the  beginning  of 
scientific  thought  by  the  help  of  which  we  gain  in- 
formation about  the  methodical  arrangement  of  our 
conceptions.  Logic  does  not  create  order  and  system 
in  our  brain,  but  it  makes  us  conscious  of  the  order 
that  naturally  grew  in  our  mind. 

The  difference  between  the  library  and  our  mind 
is,  that  in  a  library  the  shelves  have  been  put  up  be- 
fore the  books  were  stored,  but  in  our  brains  the 
different  notions  form  (or  rather  grow)  their  own 
categories.  The  notions  of  our  minds  are  like  living 
books  that  build  their  own  shelves  and  pigeon-holes, 
similar  to  the  way  in  which  cellulizing  protoplasm 
covers  itself  spontaneously  with  a  membrane.  If  we 
abstract  from   the  protoplasm,  which  constitutes  the 


20        FORM  AND  FORMAL  THOUGHT, 

contents  of  cells,  we  retain  the  empty  membranes,  and 
if  we  abstract  from  the  sensory  material  of  percepts 
and  concepts,  we  retain  their  mere  forms,  which,  re- 
duced to  rule,  are  called  formal  thought,  /.  ^.,  arith- 
metic, mathematics,  mechanics,  and  logic. 

Knowledge  of  objects  has  been  gained  by  sensory 
impressions,  but  knowledge  of  logic  can  be  acquired 
only  by  a  process  of  self-observation.  It  is  a  kind  of 
internal  experience  which  is  quite  different  from  that 
of  external  experience;  the  latter  takes  place  by,  and 
can  never  dispense  with,  the  instrumentality  of  the 
senses.  If  the  rules  of  pure  logic  are  to  be  established, 
we  must  carefully  exclude  from  this  process  of  inner 
self-contemplation  the  interference  of  the  senses,  for 
it  is  only  the  form  of  things,  and  thoughts,  and  mo 
tions,  with  which  in  purely  formal  thought  we  are  con- 
cerned. The  importance  of  these  forms  becomes  at 
once  apparent  if  we  bear  in  mind  that  as  they  are  in 
one  case  they  must  be  in  all  others  also.  The  rules 
by  which  we  generalize  our  knowledge  of  formal  con- 
ditions (of  mathematics,  arithmetic,  logic  and  mechan- 
ics) possess  universality  and  necessity. 

The  process  of  scientific  enquiry  will  be  seen  to  be 
everywhere  the  same.  Science  classifies  sensory  ex- 
perience according  to  the  categories  of  formal  thought. 
In  so  far  as  we  succeed  in  reducing  the  data  of  a  certain 
subject  to  mechanical,  mathematical,  arithmetical,  or 
logical  principles,  we  solve  its  problems  and  recognize 
why  the  different  phenomena  which  are  subject  to  our 
special  enquiry  must  be  such  as  they  are.  Science 
traces  necessity  everywhere;  and  science  can  do  so 
only  by  the  help  of  the  formal  truths,  which,  holding 
good  for  all  imaginable  cases,  show  single  instances 
under  the  aspect  of  universal  and  irrefragable  rules. 


FORM  AND  FORMAL   THOUGHT. 


21 


in. 


THE  ORDER  OF  NATURE. 


Format,  thought  represents  the  mere  laws  of  thought 
in  their  abstractness,  and  has  been  acquired  by  ab- 
straction. The  mere  forms  of  thought  exhibit  a  won- 
derful regularity  which  excites  our  admiration  all  the 
mcfre  from  the  great  advantages  man  derives  from  it. 
This  regularity  of  formal  thought,  which  is  expressed 
in  all  logical  laws,  arithmetical  calculations,  and  in  all 
mathematical  conceptions,  has  naturally  grown  in  our 
mind  as  the  psychical  expression  of  a  physical  regu- 
larity in  the  arrangement  of  the  various  brain-struct- 
ures and  their  combinations. 

The  arrangement  of  brain-structures  in  certain  reg- 
ular forms  has  been  effected  in  accordance  with  the 
same  laws  that  govern  the  development  of  forms  gen- 
erally. Therefore,  the  problem  "  why  man  happens 
to  be  a  logical  and  reasonable  being,"  turns  out  to  be 
the  same  as  that  "why  are  the  cells  in  plants  arranged 
in  a  certain  order?"  and  as  that  "why  do  crystals 
possess  a  certain  regularity?"  The  problem  common 
in  these  three  questions  is:  "Why  is  the  world  a  cos- 
mos (an  orderly  arranged  whole)  and  not  a  chaos?" 
It  is  the  same  problem  that  Kant  proposed  when  he 
asked:  "  How  is  Nature  possible  at  all?" 

The  problem  has  been  solved  differently  by  dif- 
ferent philosophers,  and  there  is  no  mark  that  better 
characterizes  a  philosophy  than  the  answer  it  pro- 
poses as  an  explanation  of  the  order  of  the  world. 
Supernaturalism  says:  The  order  of  the  world  is  due 
to  a  special  ukase  of  a  Creator.     Materialism,  on  the 


22        FORM  AND  FORMAL   THOUGHT. 


other  hand,  declares  that  order  is  the  product  of  chance. 
Both  views  have  much  more  in  common  than  appears  at 
first  sight.     Materialism  and  supernaturalism  are  an- 
tagonistic  and  their  explanations   are  irreconcilable. 
Nevertheless,  both  start  from  the  same  supposition 
which,  from  the  monistic  standpoint,  appears  to  be  er- 
roneous:  both  are  dualistic  in  so  far  as  they  consider 
the  world  as  one  thing,  and  order  as  another.     Order, 
they  declare,  has  been  imposed  upon  the  world  either 
by  a  transcendent  legislator  or   by  a   blind  chance. 
Supernaturalism  teaches  that  in  the  beginning  there 
was  iohuvabhohu,  *  the    earth    was  without  form  and 
void/  and  materialism  similarly  begins  the  history  of 
the  world  with  chaos. 

Theological  dogmatists  anthropomorphize  God  to 
such  an  extent  that  they  compare  him  to  a  watch- 
maker, and  the  world  to  a  watch.     The  order  of  the 
world,  they  imagine,  has  been  fashioned  to  his  designs. 
It  is  not  in  itself  necessary,  but  posited  by  his  will.    It 
is  necessary  only  in  so  far  as  his  intention  makes  it  so. 
On  the  other  hand,  materialistic  thinkers  similarly  ex- 
plain the  order  of  the  world,  if  not  as  the  result  of  a 
wilful  act,  yet   as  the    fortuitous   outcome  of    blind 
chance.  One  of  them  expresses  his  opinion  as  follows: 
"The  first  elements,  after  testing  every  kind  of  po- 
sition and  production  possible  by  their  mutual  unions, 
at  length  settled  in  the  form  and  way  they  now  present." 
In  opposition  to  both  views,  the  monistic  concep- 
tion considers  the  world  as  a  cosmos,  /.  e.  an  orderly 
arranged  whole.     Monism  says:    "The  world  and  the 
phenomena  of  the  world  are  orderly  arranged,  accord- 
ing to  mechanical  laws.** 

Consider  how   many   billions  of   other   combina- 
tions of  the  atoms  in  an  amoeba  are  possible,  or  at 


FORM  AND  FORMAL    TLLOUGLLT. 


23 


least  thinkable!  And  nature  should  have  tried  all 
these  infinite  possibilities,  or  part  of  them,  before  cre- 
ating the  amoeba,  and  then  the  hydra,  and  then  the 
worm,  and  so  forth!  Oh  no!  The  order  of  the  world 
is  no  hap-hazard  effect,  it  is  no  fortuitous  outcome  of 
chaos.  There  is  no  chaos  and  never  has  been  a  chaos.  L 
Even  in  the  gaseous  nebula  there  is  order  and  law, 
and  it  appears  as  chaos  only  in  comparison  to  the 
more  evolved  state  of  a  planetary  system.  Thus  the 
barbaric  stage  of  savage  life  appears  to  us  as  lacking 
in  social  order;  and  our  present  state  of  civilization,  it 
is  to  be  hoped,  will  appear  to  future  generations  as  the 
chaos  out  of  which  their  better  arranged  society 
emerged. 

Kant  says  on  this  subject:  "  The  aforementioned 
expositors  of  the  mechanical  theory  of  cosmic  genesis 
(Epicurus,  Leucippus,  and  Lucretius)  derived  every 
arrangement  perceptible  in  the  cosmic  system  from 
fortuitous  accident;  which  caused  the  atoms  so  to  hit 
together  that  they  made  up  a  well-ordered  whole.  Epi- 
curus, indeed,  was  so  presumptuous,  as  to  require  the 
atoms  to  swerve  from  their  direct  motion  without  any 
cause  at  all,  in  order  to  be  able  to  meet  one  another. 
Every  one  of  these  philosophers  carried  this  nonsensical 
principle  so  far,  as  to  ascribe  the  origin  of  all  animate 
creatures  to  this  same  blind  concurrence  of  atoms,  and 
actually  derived  reason  from  what  is  not  reason  (  Ver- 
nunft  from  Unvernunff).  In  my  system  of  science,  on 
the  contrary,  I  discover  matter  joined  to  certain  ne- 
cessary laws.  In  its  complete  dissolution  and  disper- 
sion I  see  a  beautiful  and  orderly  whole  naturally 
arising.  This  does  not  occur  through  accident  or  at 
hap-hazard,  but  it  is  seen  that  natural  properties 
necessarily  bring  it  about."     Kant  argues  that  this  ne- 


24         FORM  AND  FORMAL   THOUGHT, 

cessary  order  is  a  proof  of  the  existence  of  God.  We 
argue  from  our  standpoint  that  this  order  is  due  to  the 
laws  of  form.  It  can  be  ascertained  and  comprehended 
by  an  application  of  the  laws  of  formal  thought.  This 
order  produces,  on  the  one  hand,  the  intelligibility  of 
the  world  and,  on  the  other,  the  intelligence  of  rational 
beings.  In  its  highest  stage  this  order  appears  as  a 
moral  law  to  which  rational  beings  voluntarily  con- 
form so  as  to  be  in  unison  with  the  whole  cosmos. 
This  order,  we  maintain,  is  immanent  in  the  universe 
and,  in  fact,  //  is  God.  Human  reason  mirrors  this 
order  in  the  sentient  brain  of  a  living  being  and  thus 
the  sacred  legend  is  justified  in  declaring  that  man  hrs 
been  created  in  the  image  of  God. 

The  laws  of  order  are  omnipresent  and  eternal. 
The  omnipresence  and  eternity  of  these  laws  does  not 
denote  transcendency,  or  unknowability,  or  supernat- 
uralness.  Nothing  of  the  kind!  It  simply  means  that 
as  they  are  in  one  case,  so  are  they  rigidly  in  all  others. 
In  their  most  simple  shape,  the  laws  of  formal  thought 
(logical,  arithmetical,  mathematical,  etc.  rules)  arc 
recognized  as  self-evident  and  necessary,  so  that  we  at- 
tribute to  them  absolute  certainty  and  universality. 
The  more  complicated  processes  of  higher  algebra, 
higher  mathematics,  or  highly  involved  logical  ratio- 
cinations, appear  less  absolute  to  those  who  are  not 
familiar  with  abstract  reasoning,  but  are  after  all  just 
as  absolute.  We  are,  by  reason  of  their  complexity, 
liable  to  be  easily  mistaken,  but,  errors  on  our  part 
excluded,  they  in  themselves  are  quite  as  certain  and 
universal,  rigid  and  necessary,  as  those  simple  rules 
which  are  generally  accepted  as  axioms. 

Kant  solves  the  problem  "  How  is  Nature  possible 
at  all?  "  in  the  following  way.     The  highest  or  most 


FORM  AND  FORMAL   THOUGHT.         25 

general  laws  of  Nature,  he  argues,  are  within  us  and 
can  be  stated  a  priori,  independent  of  sensory  experi- 
ence. He  thinks  it  is  a  strange  and  wonderful  fact 
that  our  formal  thought  (the  rules  of  arithmetic, 
mathematics,  logic,  etc.,  which  are  a  priori)  agrees  so 
precisely  with  the  highest  (i.  e.,  the  most  general) 
laws  of  nature,  which  can  be  ascertained  and  verified 
a  posteriori  by  experience.  Kant  sees  only  two  ways 
of  solution.  Either  the  laws  of  pure  reason,  he  says, 
have  been  gathered  by  experience  from  nature,  or,  on 
the  contrary,  the  laws  of  nature  have  been  deduced 
from  our  a  priori  rules.  The  former  solution  is  impos- 
sible, since  the  formal  sciences  are  proven  to  have  been 
formulated  with  the  exclusion  of  all  sensory  experience. 
"Therefore,"  says  Kant,  "the  second  solution  only  re- 
mains. Reason  dictates  its  laws  to  Nature";  /.  e. 
our  reason  is  so  constituted  that  it  conceives  every- 
thing in  the  forms  of  space,  time,  and  the  categories 
of  pure  reason.  Space,  time,  and  the  categories  are 
a  part  of  the  thinking  subject,  which  cannot  but  think 
in  these  forms,  and  must  thus  transfer  them  to  the 
objects.  Our  surroundings  affect  us  by  what  we 
call  sensory  impressions.  The  sensory  impressions 
are  the  raw  material  only  from  which  the  well-ordered 
whole  of  nature,  as  an  object  of  science,  is  created  by 
the  synthetic  faculty  of  reason.  Reason  with  the  help 
of  formal  thought  shapes  this  intellectual  world  in  our 
minds,  which  is,  so  to  say,  projected  outside  of  our- 
selves into  our  surroundings. 

Kant  has  taken  into  consideration  two  ways  only. 
He  overlooked  the  third  and  most  obvious  explana- 
tion. His  explanation,  therefore,  will  be  seen  to  be 
one-sided  and  insufficient.  The  third  possibility  is  that 
which  has  been  propounded  in  the  foregoing  pages. 


■^^ 


26         FORM  AND  FORMAL    THOUGHT. 

According  to  our  explanation,  the  formal  (the  highest 
or  most  general)  laws  of  Nature  and  the  formal  laws 
of  thought  are  identical.  Their  agreement  is  not  won- 
derful but  inevitable  as  both  are  expressions  of  the 
forms  of  existence  in  general. 

Kant's  explanation  is  (me-sided,  because  if  the  for- 
mal laws  of  Nature  have  been  dictated  by  the  thinking 
subject,  it  does  not  explain  why  the  formal  thought 
(our  knowledge,  a  priori)  is  so  precisely  verified  by 
experience.  If  we  see,  as  it  were,  the  order  inio  na- 
ture, how  is  it  that  this  imposition  upon  nature  is  not 
frustrated?  Nature  is  by  no  means  pliant  to  any  fic- 
titious dictation  of  subjective  laws  a  priori.  It  frus- 
trates incorrect  a  priori  reasoning;  but  tallies  with 
correct  and  exact  calculations.  Therefore  we  conclude, 
that  the  form  of  nature  is  the  same  as  that  of  our 
reason.  The  forms  of  thought  agree  with  the  forms 
of  existence  for  the  reason  that  the  forms  of  thought 
are  only  a  special  kind  of  the  forms  of  existence. 

Kant's  explanation  is,  further,  insufficient;  it  does 
not  explain  how  formal  thought  originates.  And  this  in- 
sufficiency of  Kant's  explanation,  we  believe,  has  given 
rise  to  many  errors.  This  gap  in- Kant's  philosophy, 
we  think,  has  been  the  place  in  which  mystical  follow- 
ers of  Kant  have  been  enabled  to  construct  their  ontolog- 
ical  or  supernatural  illusions.  The  transcendental  con- 
ceptions of  pure  reason  have  been  declared  by  them 
to  be  of  transcendent*  origin.  The  opposition  of  John 
Stuart  Mill  and  his  school  to  Kant's  conception  of 
the  a  priori  arose,  as  Mr.  Mill  confesses  in  his  auto- 
biography, from  his  considering  the  transcendental 
philosophy  as  an  imposition   of   this  kind— an  impo- 

*  We  have  repeatedly  callcti  the  reader's  attention  to  the  difference  Kant 
mako  between  transcendent  (unknowable)  and  transcendental  (formal) 


FORM  AND  FORMAL   THOUGHT. 


27 


sition  by  which  inveterate  beliefs  and  deep-seated  pre- 
judices could  be  consecrated. 

According  to  our  solution,  the  radical  difference 
obtaining  between  formal  and  material  (between  what 
Kant  defines  as  a  priori  and  a  posteriori)  is  not  ne- 
glected; on  the  contrai-y,  its  fundamental  impoitance 
is  fully  recognized  and  firmly  established.  The  con- 
ception of  necessity  which  is  the  basis  of  all  science, 
has  found  its  justification  as  attaching  everywhere  to 
form — the  laws  of  form  being  everywhere  the  same. 
The  order  of  the  Universe  is  thus  recognized  as  an 
immanent  necessity.  This  necessity  can  be  traced 
with  the  assistance  of  formal  thought  everywhere, 
as  shaping  or  having  shaped  the  forms  of  exist- 
ence. The  laws  of  form  being  the  same  everywhere, 
our  reason  can,  if  not  properly  dictate,  as  Kant  says, 
yet  inform  us  about  the  form  of  existence  in  the 
whole  universe.  The  laws  of  formal  thought  being 
absolutely  and  universally  applicable,  are  our  guide 
which  like  the  thread  of  Ariadne  safely  leads  us  through 
the  labyrinth  of  the  manifold  sensory  experiences.  It 
is  this  method,  and  this  is  the  only  one,  which  frees 
philosophy  of  mysticism,  be  it  the  mysticism  of  super- 
naturalists  or  of  agnostics. 


IV. 

THE  BASIS  OF  THE  ECONOMY  OF  THOUGHT. 

Mathematics,  as  still  taught  in  our  schools,  is,  after 
the  example  of  Euclid,  unfortunately  constructed  on 
axioms.  The  introduction  of  axioms  still  gives  to 
mathematics  an  air  of  mysteriousness  which  should  be 
absent  in   this   most  reliable  and  well  established  sci- 


2g        PORM  AMD  PORMaL   1HOUGH7. 

ence.  This  doctrinal  method  of  teaching  mathematics, 
by  starting  from  authoritative  axioms,  which  have  to  be 
accepted  on  good  faith,  is  unphilosophical  and  should 
give  place  to  a  more  rational  method.  It  induced 
Schopenhauer  to  declare  that  the  whole  science,  being 
based  upon  non-proven  truths,  remains  non-proven. 
He  considers  mathematical  certainty  to  be  ultimately 
a  part  of  intuition  and  thus  reaches  a  point  where 
mysticism  can  have  full  play. 

Hermann  Grassmann  in  his  "theory  of  extension" 
{Ausdehnungsiehre)  avoids  the  faults  of  Euclid's  meth- 
od. Grassmann  throws  anew  light  upon  Kant's  idea  of 
the  a  priori  by  formulating  a  science  of  pure  mathe- 
matics. Our  space  has  three  dimensions  {Ausdehnutt- 
gen,  or  extensions),  and  plane  geometry  is  a  mathe- 
matics of  two  dimensions.  Grassmann's  idea  was,  to 
propound  mathematics  as  it  would  appear  if  absolutely 
abstracted  from  dimensions  of  any  number.  This 
science  of  pure  mathematics  must  be  the  most  ab- 
stract formal  thought.* 

The  "theory  of  forms  in  general  "  {Ailgemeitte  For- 
menlehre),  Grassmann  says,  sliould  precede  all  the 
special  branches  of  mathematics.  By  a  theory  of  forms 
in  general  he  understands  "  that  series  of  truths  which 

♦The  ingenious  attempts  of  Bolyai  and  the  Russian  geometer  Lobatschewsky 
(discussed  in  C.  F.  Gauss's  'Briefwechsel  mit  Schumacher,'  Vol.  H.  pp.  268  to 
271).  to  erect  a  geometrical  system  which  would  be  independent  of  the  Euclid- 
ian axioms  in  regard  to  parallels,  and  Riemann's  meritorious  essay  ••  On  The 
Hypotheses  Of  Geometry,"  have  called  the  attention  of  mathematicians  and 
scientists  to  a  remarkable  problem  which  finds  its  natural  and  most  simple 
solution  in  Grassmann's  theory  of  pure  mathematics.  Hamilton's  method  of 
Quaternions  is  contained  in  it  also,  since  Grassmann  takes  into  account  the 
length  and  direction  of  lines.  For  brief  information  on  the  subject  see 
Helmholtz's  lucid  sketch  Ueber  die  Tkattaehen,  die  d4r  Geomftrif  zu  Grunde 
liegen  (Upon  the  Facts  that  lie  at  the  Basis  of  Geometry).  J.  B.  Stallo.  "  The 
Corcapta  and  Theories  of  Modern  Phy?;ics.  '  pp.  208  seqq..  and  24H  sjqq..  and 
comr  are  also  with  Hermann  Grassiuanu  Ausdehnungsiehre.  Anhuu^il.  and 
111.  pp.  27 J  seqq.,  and  277  st>qq. 


FORM  AND  FORMAL   THOUGH!.         29 

refers  equally  to  all  branches  of  mathematics  and 
which  presupposes  only  the  general  concepts  of  identity 
and  difference,  of  combination  and  separation.  *  * 
Products  of  thought  can  originate  in  two  ways,  either 
by  a  simple  creative  act  (that  of  positing)  or  by  the 
double  act  of  positing  and  combining.  The  product 
of  the  former  kind  is  a  constant  form  or  magnitude 
in  a  narrower  sense,  that  of  the  latter  kind  is  a  dis- 
crete form  or  a  form  of  combination." 

On  the  concepts  of  the  identity  and  difference  of  po- 
sited acts  of  thought  by  mere  combination  and  separa- 
tion, Grassmann  builds  his  magnificent  structure  of  a 
theory  of  forms  in  general,  of  which  arithmetic,  geom- 
etry, algebra,  mechanics,  phoronomics,  and  logic  appear 
to  be  applications  only  of  special  kinds.  He  is  in  need 
of  no  axioms  whatever.  The  only  postulates  are  such 
as  these:  Arithmetic  is  a  system  of  first  degree;  plane 
geometry  is  a  system  of  second  degree;  and  space  is  a 
system  of  third  degree.  Plane  geometry  has  two  di- 
mensions, and,  therefore,  if  we  have  one  point  fixed, 
two  magnitudes  are  required  for  the  determination  of 
any  other  point.  Space  has  three  dimensions,  so  that 
taking  a  fixed  point  three  magnitudes  are  necessary 
for  the  determining  of  any  other  point.  Colors,  it  ap- 
pears, are  another  system  of  third  degree;  they  can  be 
reduced  to  three  primary  colors:  red,  orange,  and  blue. 
Accordingly  three  magnitudes  are  required  for  deter- 
mining any  kind  of  tint.  A  distinguished  scientist  has 
invented  a  method  of  graphic  representation  of  colors 
by  triangles.  . 

We  cannot  have  any  intuitive  conception  of  a  space 
having  four  dimensions.  Nevertheless,  pure  mathemat- 
ics, being  independent  of  dimensions,  applies  just  as 
much  to  systems  of  four  and   more   degrees  as  to  the 


so        POMM  AND  FORMAL   THOUGHT. 

actual  space  of  three  dimensions.  The  regularity  of 
every  system  is  fixed  a  priori  by  the  elements  posited 
for  that  system.  The  elements,  positing  themselves  or 
being  posited  by  us  according  to  the  rigid  rule  of  strict 
consistency,  will  necessarily  form  a  regular  and  order- 
ly arranged  system.  We  can  therefore  state  with  ab- 
solute precision  all  the  formal  laws  by  which  bodies  of 
four  or  five  dimensions,  if  they  existed,  would  be  gov- 
erned.* 

The  chief  difference  between  the  numbers  of 
arithmetic,  geometrical  planes,    mathematical  space, 

♦  As  an  example  we  may  use  the  instance,  that  the  product  of 
two  magnitudes  in  a  system  of  second  degree  can  be  algebraically 
expressed  by 

(a  +  b)*  —  a"  +  2ab  +  b^ 
in  a  system  of  third  degree,  by 

(a  +  bf  —  a^  +  3a*b  +  jab'  +  b" 
m  a  system  of  fourth  degree,  by 

(a  +  b)*  —  a*  +  4an)  +  Ga'b''  +  4ab'  +  b*. 

Accordingly,  a  cube  or  any  parallelopipedon  which  is  the 
product  of  two  magnitudes  consists  of  eight  tri-dimensional  parts. 
This  fact  cannot  only  be  proven  a  priori  by  mathematical  or  alge- 
braical demonstration  of  purely  formal  thought,  it  can  be  ascer- 
tained by  experience  also.  A  cube  that  is  cut  in  all  its  three  di- 
mensions, according  to  the  ratio  of  a  +  b.  will  afford  an  example, 
and  a  body  formed  by  two  magnitudes  (a  +  b)  in  four  dimensions, 
if  it  were  possible,  would  consist  of  the  following  i6  four-dimensional 
parts: 

1.  A    regular    body   which   m   all    four   directions   measures 

2.  Another  regular  body  which  in  all  four  directions  measures 

3.  Four  bodies  which  in  three  dimensions  measure  a  (—  a'),  and 
in  one  b 

4.  Four  bodies  which  in  three  dimensions  measure  b  (—b'),  and 
in  one  a, 

5)  Six  bodies  which  in  two  (Mmensions  measure  n  (—  a'),  and 
in  two  /'  (—  b')^ 


FORM  A  ND  FORMA  L   I  HO  UGHT.         3 1 

on  the  one  hand,  and  Grassmann's  systems  of  i,  2,  3, 
or  n  dimensions  on  the  other,  is,  that  numbers,  planes, 
and  actual  space  are  accepted  as  given;  they  are  the 
data  of  arithmetic,  geometry,  and  mathematics,  while 
the  systems  constructed  by  Grassmann's  "theory  of 
forms  in  general"  are  conceived  as  products  of  thought. 
They  are  posited  by  a  progress  of  thought  and  can  be 
considered  as  data  only  if  their  parts,  once  posited,  are 
further  used  as  such  for  combinations  among  them- 
selves. 

It  is  obvious  that  the  only  condition  of  all  kinds  of 
such  systems  of  formal  thought  is  consistency.  Truth 
with  regard  to  our  knowledge  of  reality  is  the  agree- 
ment of  our  concepts  with  the  objects  represented; 
but  truth  in  the  domain  of  pure  formal  thought  is  the 
agreement  of  all  posited  forms  of  one  and  the  same 
system  among  each  other.  This  consistency  is  the 
basis  of  all  law,  regularity,  and  order;  and  whatever 
system  of  forms  may  be  selected,  its  rules  and  theo- 
rems will  be  developed  by  our  mind  with  the  same 
wonderful  harmony  and  precision  as  can  be  observed  in 
mathematics,  arithmetic,  logic,  and  mechanics.  Ac- 
cordingly, if  the  world  were  otherwise  than  it  is,  if 
space  had  only  two,  or  if  it  had  four  dimensions,  the 
laws  of  the  world  would  be  otherwise,  but  none  the  less 
regular  than  at  present — they  would  be  strictly  gesetz- 
mdssig,  i.  e.,  conforming  to,  and  explainable  by,  law. 

Consistency  must  be  considered  in  the  empire  of 
form  as  the  counterpart  of  inertia*  in  the  realm  of  mat- 
ter. So  long  as  nothing  interferes  to  produce  a  change, 


♦  Inertia  in  German  is  sometimes  called  Triigheit,  sometimes  Be/tarrung-. 
Tragheit  is  the  literal  translation  of  inertia;  it  is  a  negative  term  which  de- 
notes the  non-appearance  of  new  energy,  or  motion,  or  activity.  Beharrung 
is  the  better  term;  it  affords  a  positive  expression  for  "  inertia,"  denoting  the 
ur.changed  continuance  of  the  energy  in  existence. 


hi 


32 


FORM  AND  FORMAL   THOUGHT. 


everything  will  remain  as  it  is.  Consistency  therefore, 
the  very  root  of  order,  from  which  all  order  of  form  in 
every  possible  system  of  forms  finds  its  explanation,  is. 
the  natural  state.  Consistency  like  the  law  of  inertia 
and  the  law  of  identity  explains  itself.  Wherever  we 
meet  with  it,  it  need  not  be  accounted  for;  an  expla- 
nation becomes  necessary  only  where  consistency  is 
lacking.  From  this  consideration  it  is  apparent  that 
to  whatever  system  the  form  of  reality  belonged,  it 
could  in  no  case  be  devoid  of  order.  The  world  could 
not  be  a  chaos,  but  of  necessity  must  be  a  cosmos. 

Grassmann's  theory  of  'forms  in  general'  throws  a 
new  light  upon  Kant's  doctrine  of  the  a  priori,  since  it 
exhibits  a  science  of  pure  form  in  its  most  generalized 
abstractness.  Thus  the  a  priori  has  lost  the  last  ves- 
tige  of  mystery  and  we  can  easily  understand  how  the 
cosmical  order  is  due  to  the  formal  laws  of  nature. 
While  Kant's  reasoning  has  been  correct  in  the  main, 
it  is  apparent  that  real  space  is  not  quite  so  purely 
formal  as  he  imagined.  A  system  of  form  of  the  third 
degree  can  be  posited  a  priori  by  formal  thought;  but 
the  fact  that  real  space  is  such  a  system  of  the  third 
degree  can  be  ascertained  by  experience  only. 

We  have  used  the  word  order  in  the  sense  of  ob- 
jective regularity  which  of  necessity  results  from  a 
consistency  of  form  throughout  one  and  the  same  sys- 
tem. This  regularity  of  forms  enables  us  to  think 
many  samenesses  by  one  idea  and  thus  makes  an 
economy  of  thought  possible,  which  as  Ernst  Mach  de- 
clares  is  the  characteristic  feature  of  science.  Ernst 
Mach  (who  I  must  suppose  has  attained  to  his  ideas 
quite  independently  of  Grassmann,  although  there  is 
no  doubt  that  both  have  been  strongly  influenced  by 
Kant),  points  out,  by  a  happy  instinct  as  it  were,  the 


FORM  AND  FORMAL   THOUGHT.         33 

most  practical  application  of    the   theory  of  formal 
thought  in  general. 

The  regularity  of  form  being  repeated  in  the  phy- 
siological arrangement  of  the  nervous  cells  and  fibres 
in  our  brain,  produces  in  man  an  economy  of  feeling 
and  thinking  which  the  more  it  is  realized  and  prac- 
ticed, gives  him  the  greater  power  over  nature. 


V. 


CONCLUSION. 

Although  Kant's  Transcendental  Idealism  cannot 
be  considered  as  a  final  solution  of  the  basic  problem 
of  philosophy,  it  nevertheless  pursues  the  right  method 
and  has  thus  actually  led   us   to   a   solution  which,  we 
hope,  will  in  time  be  recognized  as  final.     In  Kant's 
time,  it  seemed  as  if  the  key  to  the  mysteries  of  cos- 
mic order  should  be  sought  for  in  nature's  manifesta- 
tions outside  of  the  human  mind.    Kant,  a  second  Co- 
pernicus, reversed  the  whole  situation    and  pointed 
out  that  the  key  to  the  problem:    "  How  is  nature  pos- 
sible at  all?"  is  to  be  found  in  the  human  mind.     And 
yet  the  natural  sciences,   inquiring  into  the  secrets  of 
nature  by  the  observation  of  natural  phenomena,  were 
after  all  not  on  a  wrong  track.     Kant  and  the  natural 
sciences  seemed  to  exclude  each  other,  but  they  were 
complementary.      Schiller  who  in  so   many  respects 
fore-felt  and  fore-told  future  events  in  the  prophetic 
spirit  of  his  poetry,  said   in  one  of  his  Xenions,  re- 
ferring to    Transcendental    Philosophy    and  Natural 
Science : 

"  Both  have  to  travel  their  ways,  though  the  one  should  not  know  of  the  other. 
Each  one  must  wander  on  straight,    and  in  the  end  they  will  meet  " 

Two   truths    may    at   first   appear   contradictory, 


34         FORM  AND  FORMAL    THOUGHT. 

though  they  are  not.  Let  us  not  distort  the  one  for 
the  sake  of  the  other,  but  let  each  be  presented  with- 
out regard  to  the  other,  and  let  every  point  of  diver- 
gency be  brought  out  fully.  Theory  and  practice, 
formal  thought  and  experience,  the  thinker  and  ob- 
server, will  at  last  agree  better  if  they  boldly  take  the 
consequences  of  their  views  and  combat  those  of  the 
other.  About  the  relation  of  transcendental  philoso- 
phy to  natural  science  in  his  time,  Schiller  said: 

•'  Enmity  be  between  both,  your  alliance  would  not  be  in  time  yet. 

Though  you  may  separate  now.  Truth  will  be  found  by  your  search." 

There  has  been  enmity  enough  between  philosophy 
and  natural  science.  Philosophers  looked  with  scorn 
upon  the  specialists  who  confined  their  labors  to  nar- 
row circles,  and  scientists,  confident  of  their  positive 
results,  smiled  about  the  phantastic  dreams  of  theo- 
retic speculations.  However,  in  the  progress  of  time, 
philosophers  learned  to  prize  the  valuable  researches 
of  natural  science,  and  the  scientists  felt  the  necessity 
of  a  philosophical  basis  for  their  investigations  and 
methods  of  investigation.  At  present  the  want  of  a 
close  contact  between  philosophy  and  the  sciences  is  a 
fact  that  is  freely  acknowledged  by  both,  philosophers 
and  scientists. 

In  Kant's  and  in  Schiller's  time  an  alliance  be- 
tween philosophy  and  natural  science  would  have  been 
premature.  How  many  futile  attempts  have  been  made 
in  the  mean  time!  Fichte,  Schelling,  Hegel,  and 
Schopenhauer  in  Germany,  the  two  Mills  and  Herbert 
Spencer  in  England,  Auguste  Comte  in  France,  have 
appeared  with  their  systems,  partly  opposing,  partly 
repeating  Kantian  ideas  in  other  and  original  ways  of 
presentation,  partly  combating  his  very  method,  partly 
popularizing,  and  at  the  same  time  opposing  his  views. 


FORM  AND  FORMAL   THOUGHT.        35 

But  none  of  them  (not  even  Comte*)  succeeded  in 
creating  a  well-established  positivism  that  could  dis- 
pense with  the  mystical  element  altogether,  whether 
it  appear  as  the  Transcendent,  the  Unknowable,  or 
the  Supernatural. 

We  have  attempted  in  these  essays  on  "  Form  and 
Formal  Thought "  to  lay  the  cornerstone  of  such  posi- 
tivism, which,  it  is  to  be  hoped,  will  prove  to  be  the 
only  true  Monism,  /.  ^.,  a  philosophy  free  from  contra- 
dictions and  in  accordance  with  reality,  thus  offering 
a  basis  for  a  unitary  and  harmonious  conception  of  the 
world. 


•  Comte  believed  in  the  Unknowability  of  what  he  called  "  first  and  final 
causes,"  and  considered  only  "the  middle  between  them  "  accessible  to  cog- 
nition. He  attempted  to  limit  science  to  the  positively  knowable,  but  m  so 
doing  he  left  a  non-knowable;  he  did  not  succeed  in  entirely  freeing  himself 
from  mysticism— which  after  all  is  the  primary  object  of  all  philosophy. 


THE   OPEN    COURT. 

PUBLISHED  EVERY  THURSDAY  BY 

THE  OPEN  COURT  PUBLISHING  COMPANY. 

CHICAGO.  ILL. 

p.  a  DRAWER  F.  169—175  La  Salle  Street. 


EDWARD  C.  HEGELER.  Pres.— Dr.  PAUL  CARUS,  Editor. 


The  reader  will  find  in  The  Open  Court  an  earnest  and.  as  we  believe,  a 
taccessful  effort  to  conciliate  Religion  with  Science  The  work  is  done  with 
dne  reverence  for  the  past  and  with  full  confidence  in  a  hipher  future. 

The  Opem  Court  unites  the  deliberation  and  prudence  of  conservatism 
with  the  radicalism  of  undaunted  proRress.  While  the  merits  of  the  old  creeds 
are  folly  appreciated,  their  errors  are  not  overlooked.  The  ultimate  conse- 
quences of  the  most  radical  thouRht  are  accepted,  bat  care  is  taken  to  avoid 
the  lanlti  of  a  onesided  view. 

THE  QUINTESSENCE  OF  RELIGION 

is  shown  to  be  a  truth.  It  is  a  scientific  truth  (a  reality)  which  has  been  and 
will  remain  the  basis  of  ethics  The  Quintessence  of  Religion  contains  all  that 
is  good  and  true,  elevating  and  comforting,  in  the  old  religions.  Superstitious 
notions  are  recognized  as  mere  accidental  features,  of  which  Religion  can  be 
porifaed  without  harm  to  the  properly  religious  spirit. 
This  idea  is. 

FEARLESSLY  AND  WITHOUT  RESERVATION  OF  ANY  KIND, 

presented  in  its  various  scientific  aspects  and  in  its  deep  significance  to  in- 
tcltectnal  and  emotional  life.  If  fully  grasped,  it  will  be  found  to  satisfy  the 
yearnings  of  the  heart  as  well  as  the  requirements  of  the  intellect. 

Facts  which  seem  to  bear  unfavorably  on  this  solution  of  the  religious 
problem  are  not  shunned,  but  openly  faced  Criticisms  have  been  welcome, 
and  will  always  receive  due  attention.  The  severest  criticism,  we  trust,  will 
serve  only  to  elucidate  the  truth  of  the  main  idea  propounded  in  The  Opeh 
Court. 

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Publications  of  The  Open  Court  Publishing  Co. 

THREE  INTRODUCTOKY  LECTURES  ON  THE 
SCIENCE  OF  THOUGHT. 

Delivered  at  the  Royal  Institution,  London,  during  the  month  of 
March,  1887.  First  published  in  The  Open  Court  of  June, 
July,  and  August,  1887.  By  F.  Max  Miiller.  With  an  Ap- 
pendix which  contains  a  Correspondence  on  "Thought  with- 
out Words,"  between  F.  Max  Miiller  and  Francis  Galton,  the 
Duke  of  Argyll,  George  J.  Romanes  and  others.  Price, 
75  Cents.     The  book  contains  three  essays  : 

1.  The  Simplicity  of  Language  ; 

2.  The  Identity  of  Language  ;  and 

3.  The  Simplicity  of  Thought. 

The  Appendix  consists  of  Max  MUller's  Correspondence  on 
' '  Thought  without  Words "  with  Mr.  George  Romanes,  the 
Duke  of  Argyll,  etc.  Max  MUller's  essays  must  not  only  be 
read,  they  must  be  studied  ;  and  we  should  be  very  grateful 
that  the  eminent  philologist  uses  such  simple  language.  In 
spite  of  all  the  simplicity  of  Max  Miiller's  style,  it  takes  much 
careful  study  to  fathom  the  depths  of  his  thoughts.  The  study 
of  language  is  of  interest  to  the  lawyer  as  well  as  the  clergy- 
man, the  scientist  as  well  as  the  teacher,  and  no  education  is 
complete  without  it. 

THE  H)EA  OF  GOD. 

By  Paul  Car  us,  Ph.  D.  Price,  15  Cents.  Contents  :  The  Nature 
of  Ideas— The  Etymology  of  the  Word  God— God  an  Abstract 
Idea.— The  Conceptions  of  God  (Polytheism,  Monotheism. 
Deism,  Pantheism,  Atheism)— Definition  of  the  Idea  of  God 
(Entheism— Concluding   remarks  on  Worship  and  Prayer). 

THE  PSYCHIC  LIFE  OF  MICRO-ORGANISMS. 

A  Study  in  Experimental  Psychology.  By  Alfred  Binet.  Trans- 
lated from  the  French  by  Thomas  McCormack,  with  a  preface 
by  the  author  written  especially  for  the  American  edition. 
Cloth,  75  Cents.  The  work  contains  the  most  important  re- 
sults of  recent  investigations  into  the  world  of  Micro-Organ- 
isms,  a  branch  of  comparative  psychology  little  known  ;  as  the 
data  of  this  department  of  natural  science  lie  scattered  for  the 
most  part  in  isolated  reports  and  publications,  and  no  attempt 
has  hitherto  been  made  to  present  them  in  a  systematized  form. 
M.  Binet *s  researches  and  conclusion  show,  "that  psycho- 
logical phenomena  begin  among  the  very  lowest  classes  of 
beings."  The  author  contests  the  theory  of  the  distinguished 
English  scientist,  Prof.  George  J.  Romanes,  who  assigns  the 
first  appearance  of  the  various  psychical  and  mental  faculties 
to  different  stages  or  periods  in  the  scale  of  zoological  devel- 
opment. To  M.  Binet  there  is  an  aggregate  of  properties 
which  exclusively  pertain  to  living  matter,  the  existence  of 
which  is  seen  in  the  lowest  forms  of  life  as  well  as  in  the  highest. 


Published  Simultaneously  with  this  Pamphlet: 

Fundamental  Problems. 


THE 


Metbod  of  Pbilosophy  as  a  Systematic  Airangement  of  Knowledge 


BY 


DR.  PAUL  CARUS. 


No  Agnosticism  but  Positive  Science^ 
No  Mysticism  but  Clear  Thought, 

Neither  Sm/eruaturalism  nor  Materialism^ 
But  a  Unitary  Conception  of  the  World, 

No  Dogma  but  Religion, 
No  Creed  but  Faith. 


TABLE  OF  CONTENTS. 


Sensation  and  Memory— Cognition,  Knowledge,  and  Truth— The  Foundation 
of  Moniam— Form  and  Formal  Thought :  I.  Kant's  Critique  of  Pure 
Reason;  IL   The  Origin  of   the 'A  Priori';  III.   The  Order  of  Nature; 

IV.  The  Basis  of  the  Economy  of  Thought.— The  Old  and  the  New  Math- 
ematics—Metaphysics :  the  Use  and  Meaning  of  the  Word. 

The  Problem  of  Causality— Matter.  Motion,  and  Form— Unknowability  and 
Causation— Causes  and  Natural  Laws— Is  Nature  Alive  ?  I.  The  Univer- 
sality of  Life  ;  II.  Can  the  World  be  Mechanically  Explained?  III.  The  Ele- 
ments Explainable  by  Form  ;  IV.  Machines  and  Organisms ;  V.  Organized 
and  Psychical  Life—Cause,  Reason,  and  End. 

The  Idea  of  Absolute  Existence  :  I.  The  Veil  of  Maya  :  II.  Agnosticism  and 
Phenomenalism;  III.  Goethe's  Monism ;  IV.  Phenomena  and  Noumena; 

V.  The  Oneness  of  the  Phenomenal  and  the  Noumenal ;  VI.  God  as  the 
Moral  Law. 

The  Stronghold  of  Mysticism:  I.  The  Unknowable;  II.  The  Fashionable 
Mysticism  of  the  Day ;  III.  The  Infinite  a  Mathematical  Term  ;  IV.  Is  the 
Infinite  Mysterious ;  V.  Space  and  Time ;  VI.  Infinitude  and  Eternity- 
Idealism  and  Realism. 

Hedonism  and  Asceticism— Causation  and  Free  Will— The  Oneness  of  Man 
and  Nature— Ethics  and  Natural  Science— Christ  and  His  Ethics— No 
Creed  but  Faith— The  Importance  of  Art— Tragedy  and  the  Problem  of 
Evil— Classical  and  Romantic  Art. 

THE  OPEN  COURT  PUB.  CO., 

169-175  LA  SALLE  STREET,  CHICAGO.  ILL. 


